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Search: id:A007782
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| A007782 |
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Factors in the infinite word formed by the Kolakoski sequence A000002. |
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+0
1
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| 2, 4, 6, 10, 14, 18, 26, 34, 42, 50, 62, 78, 94, 110, 126, 142, 162, 186, 218, 250, 282, 314, 346, 378, 410
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) = number of different substrings of length n found in Kolakoski sequence A000002. It is conjectured that a(n) grows like n^(log(3)/log(3/2)).
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REFERENCES
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M. Dekking: "What is the long range order in the Kolakoski sequence?" in: The Mathematics of Long-Range Aperiodic Order, ed. R. V. Moody, Kluwer, Dordrecht (1997), pp. 115-125.
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LINKS
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D. Wilson, Table of n, a(n) for n=1,...,100.
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EXAMPLE
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For length 3 only the strings 11, 121, 211, 221, 212, 122 occur, so a(3) =6. For length 4 only the 10 strings 1121, 1122, 1211, 1212, 1221, 2112, 2121, 2122, 2211, 2212 occur.
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CROSSREFS
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Sequence in context: A024518 A128422 A098380 this_sequence A035501 A024204 A036641
Adjacent sequences: A007779 A007780 A007781 this_sequence A007783 A007784 A007785
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KEYWORD
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nonn,hard,nice
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AUTHOR
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Patricia Lamas (lamas(AT)math.uqam.ca)
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EXTENSIONS
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Additional comments from Michael Baake (mbaake(AT)pion09.tphys.physik.uni-tuebingen.de), Feb 19, 2001.
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